user2001: In a Queen + King versus Queen + King endgame (including zero or more pawns) these is a strong draw tendency due to the fact that a Queen can deliver multiple checks in a row to the opponents open King. My question concerns the Queen+pawn versus Queen endgame. Assuming that the pawn is on its initial square (second rank for white, seventh rank for black), are all these endgames objectively drawn? Second of all, what is the best strategy for the player with the material advantage to aim for a win?

user2300: This ending is a draw unless the pawn is a bishop pawn or a central pawn  and the pawn is in the seventh rank and is supported by its king. If the defending king can get in front of the pawn, the game is a draw; otherwise it is best for the defender to keep his king far away from the pawn. The defender should keep checking until he runs out of check, and then pin the pawn (a good strategy to draw). Based on computer analysis, there is a different thinking :normally the defending king needs to be in front of the pawn. A rook pawn or knight pawn is a theoretical draw if the defending king is in front or near the pawn or if the king is in the corner opposite the pawn's promotion square. A knight pawn has more practical winning chances than a rook pawn. A bishop pawn or central pawn is a win if the defending king is not in front of the pawn. A bishop pawn has better winning chances than a central pawn. The position of the defending king is especially important .
Edmar Mednis gave this breakdown when the defending king is not able to help:

A bishop pawn is the best pawn to have. It is relatively easy to advance and is a win once it reaches the seventh rank.
A central pawn wins if it reaches the seventh rank, but it is difficult to get it there.
if the pawn reaches the sixth rank, the position is usually a draw.
A knight pawn is relatively easy to get to the seventh rank, but the position may be a    theoretical draw.
Positions with rook pawns are theoretical draws, but in practice it may be difficult to draw 

John Nunn gives this summary for the defense:
with a central pawn, the defense has two possibilities: get the king in front of the pawn or get the king to corner nearest to the pawn's promotion square
with a bishop pawn, the defender's only chance is to get the king in front of the pawn
with a knight pawn, the defender must get the king in front of the pawn or in the corner furthest from the promotion square
a rook pawn is generally a draw and the defensive guidelines are the same as for a knight pawn.
Naturally, the less advanced the pawn is, the better the defensive chances 

user872: According to Wikipedia:

According to Reuben Fine and Pal Benko, this ending is a draw unless
  the pawn is a bishop pawn or a central pawn (i.e. king pawn or queen
  pawn) and the pawn is in the seventh rank and is supported by its
  king. If the defending king can get in front of the pawn, the game is
  a draw; otherwise it is best for the defender to keep his king far
  away from the pawn.

If this endgame needs all those conditions to be winning, and you are saying that 

"pawn is on its initial square"

I would claim (based on the Reuben Fine and Pal Benko conditions) that this endgame is a draw unless you have a forced way to trade queens and to guarantee that your king gets to control the critical squares. For example:

From my example above you can see that these endgames are not always a draw, but apart from that type of situation, it will be a draw more often than not.

user2042: 
My question concerns the Queen+pawn versus Queen endgame. Assuming that the pawn is on its initial square (second rank for white, seventh rank for black), are all these endgames objectively drawn? Second of all, what is the best strategy for the player with the material advantage to aim for a win?

Emphasis above are mine, and since you have 2 questions I shall answer both separately.

are all these endgames objectively drawn?

No they are absolutely not!

Second of all, what is the best strategy for the player with the material advantage to aim for a win?

Without seeing the exact position I can not answer that-your question is too broad-these endgames require thorough study as everything counts there ( the position of the kings, who moves first and so on ). 
I can recommend you Yuri Averbakh-Comprehensive Chess Endings ( Volume 3 ) to learn how to win Q+P+K vs K+Q endgames. There you have described patterns for winning with the bishop/knight/rook/central pawn, queen and king vs king and queen. 
I have just suggested the above book because it is written for all levels of play-from novice up to grandmaster-so with that knowledge you can not squander your edge, but if you find something else even better for you! 
The key is just to learn how to recognize winning position and to learn how to win it.
All you have to do now, is to use this tablebase to see how can you reach the winning position.
If you have trouble finding exact winning moves you can always go through tablebase moves-just click on the notation.
SUMMARY:
Learn how to win Q+P+K vs K+Q endgames->input the position you are interested in into tablebase->if winnable, play through moves to see how to reach winning position.
I know that this might be too broad of an answer to you, but you ask for help in Queen endgames and these are the toughest to master. Just one imprecise move ( not to mention wrong one ) gives your opponent a draw and squanders your edge! 
Hopefully this answer helped you a little.
If you have further question leave a comment and I will reply.
Best regards.

2001: <p>In a Queen + King versus Queen + King endgame (including zero or more pawns) these is a strong draw tendency due to the fact that a Queen can deliver multiple checks in a row to the opponents open King. My question concerns the Queen+pawn versus Queen endgame. Assuming that the pawn is on its initial square (second rank for white, seventh rank for black), are all these endgames objectively drawn? Second of all, what is the best strategy for the player with the material advantage to aim for a win?</p>
 2300: <p>This ending is a draw unless the pawn is a bishop pawn or a central pawn  and the pawn is in the seventh rank and is supported by its king. If the defending king can get in front of the pawn, the game is a draw; otherwise it is best for the defender to keep his king far away from the pawn. The defender should keep checking until he runs out of check, and then pin the pawn (a good strategy to draw). Based on computer analysis, there is a different thinking :normally the defending king needs to be in front of the pawn. A rook pawn or knight pawn is a theoretical draw if the defending king is in front or near the pawn or if the king is in the corner opposite the pawn's promotion square. A knight pawn has more practical winning chances than a rook pawn. A bishop pawn or central pawn is a win if the defending king is not in front of the pawn. A bishop pawn has better winning chances than a central pawn. The position of the defending king is especially important .</p>

<p>Edmar Mednis gave this breakdown when the defending king is not able to help:</p>

<ol>
<li>A bishop pawn is the best pawn to have. It is relatively easy to advance and is a win once it reaches the seventh rank.</li>
<li>A central pawn wins if it reaches the seventh rank, but it is difficult to get it there.</li>
<li>if the pawn reaches the sixth rank, the position is usually a draw.</li>
<li>A knight pawn is relatively easy to get to the seventh rank, but the position may be a    theoretical draw.</li>
<li>Positions with rook pawns are theoretical draws, but in practice it may be difficult to draw </li>
</ol>

<p><strong>John Nunn gives this summary for the defense:</strong></p>

<p>with a central pawn, the defense has two possibilities: get the king in front of the pawn or get the king to corner nearest to the pawn's promotion square
with a bishop pawn, the defender's only chance is to get the king in front of the pawn
with a knight pawn, the defender must get the king in front of the pawn or in the corner furthest from the promotion square
a rook pawn is generally a draw and the defensive guidelines are the same as for a knight pawn.
Naturally, the less advanced the pawn is, the better the defensive chances </p>
 872: <p>According to Wikipedia:</p>

<blockquote>
  <p>According to Reuben Fine and Pal Benko, this <strong>ending is a draw unless</strong>
  the <strong>pawn is a bishop pawn</strong> or a <strong>central pawn</strong> (i.e. king pawn or queen
  pawn) and the pawn is <strong>in the seventh rank</strong> and is supported by <strong>its
  king</strong>. If the defending king can get in front of the pawn, the game is
  a draw; otherwise it is best for the defender to keep his king far
  away from the pawn.</p>
</blockquote>

<p>If this endgame needs all those conditions to be winning, and you are saying that </p>

<blockquote>
  <p>"pawn is on its initial square"</p>
</blockquote>

<p>I would claim (based on the Reuben Fine and Pal Benko conditions) that this endgame is a draw unless you have a forced way to trade queens and to guarantee that your king gets to control the critical squares. For example:</p>

<p><img src="https://i.stack.imgur.com/qiGRa.png" alt="Example"></p>

<p>From my example above you can see that these endgames are not always a draw, but apart from that type of situation, it will be a draw more often than not.</p>
 2042: <blockquote>
  <p>My question concerns the Queen+pawn versus Queen endgame. Assuming that the pawn is on its initial square (second rank for white, seventh rank for black), <strong>are</strong> all these endgames objectively drawn? Second of all, <strong>what is the best strategy for the player with the material advantage</strong> to aim for a win?</p>
</blockquote>

<p>Emphasis above are mine, and since you have 2 questions I shall answer both separately.</p>

<blockquote>
  <p>are all these endgames objectively drawn?</p>
</blockquote>

<p>No they are absolutely not!</p>

<blockquote>
  <p>Second of all, what is the best strategy for the player with the material advantage to aim for a win?</p>
</blockquote>

<p>Without seeing <strong>the exact position</strong> I can not answer that-your question is too broad-these endgames require thorough study as <strong>everything counts</strong> there ( the position of the kings, who moves first and so on ). </p>

<p>I can recommend you <em>Yuri Averbakh-Comprehensive Chess Endings ( Volume 3 )</em> to learn how to win <code>Q+P+K</code> vs <code>K+Q</code> endgames. There you have described patterns for winning with the bishop/knight/rook/central pawn, queen and king vs king and queen. </p>

<p>I have just suggested the above book because it is written for all levels of play-from novice <strong>up to grandmaster</strong>-so with that knowledge you can not squander your edge, but if you find something else even better for you! </p>

<p>The key is just to learn how to <strong>recognize winning position and to learn how to win it.</strong></p>

<p>All you have to do now, is to use <a href="http://www.k4it.de/index.php?topic=egtb&amp;lang=en" rel="noreferrer">this <code>tablebase</code></a> to see <strong>how can you reach the winning position.</strong></p>

<p>If you have trouble finding <strong>exact</strong> winning moves you can always go through <code>tablebase</code> moves-just click on the notation.</p>

<h2>SUMMARY:</h2>

<p>Learn how to win <code>Q+P+K</code> vs <code>K+Q</code> endgames->input the position you are interested in into tablebase->if winnable, play through moves to see how to reach winning position.</p>

<p>I know that this might be too broad of an answer to you, but you ask for help <strong>in Queen endgames</strong> and these are the toughest to master. Just one <strong>imprecise move</strong> ( not to mention wrong one ) gives your opponent a draw and squanders your edge! </p>

<p>Hopefully this answer helped you a little.</p>

<p>If you have further question leave a comment and I will reply.</p>

<p>Best regards.</p>
