[@pacard] can be found in the literature. This paper uses the DPW method in ${\mathbb{H}}^3$ to construct these surfaces. The two resulting theorems are as follows.

\[theoremConstructionNnoids\] Given a point $p\in{\mathbb{H}}^3$, $n\geq 3$ distinct unit vectors $u_1, \cdots, u_n$ in the tangent space of ${\mathbb{H}}^3$ at $p$ and $n$ non-zero real weights $\tau_1,\cdots,\tau_n$ satisfying the balancing condition $$\label{eqBalancingNnoids}
    \sum_{i=1}^{n}\tau_i u_i = 0$$ and given $H>1$, there exists a smooth $1$-parameter family of CMC $H$ surfaces $\left(M_t\right)_{0<t<T}$ with genus zero, $n$ Delaunay ends and the following properties:

1.  Denoting by $w_{i,t}$ the weight of the $i$-th Delaunay end, $$\lim\limits_{t\to 0} \frac{w_{i,t}}{t} = \tau_i.$$

2.  Denoting by $\Delta_{i,t}$ the axis of the $i$-th Delaunay end, $\Delta_{i,t}$ converges to the oriented geodesic through the point $p$ in the direction of $u_i$.

3.  If all the weights $\tau_i$ are positive, then $M_t$ is Alexandrov-embeddedd.

4.  If all the weights $\tau_i$ are positive and if for all $i\neq j\in[1,n]$, the angle $\theta_{ij}$ between $u_i$ and $u_j$ satisfies $$\label{eqAnglesNnoid}
            \left| \sin\frac{\theta_{ij}}{2} \right|>\frac{\sqrt{H^2-1}}{2H},$$ then $M_t$ is embedded.

\[theoremConstructionMinoids\] Let $M_0\subset{\mathbb{R}}^3$ be a non-degenerate minimal $n$-noid with $n\geq 3$ and let $H>1$. There exists a smooth family of CMC $H$ surfaces $\left(M_t\right)_{0<|t|<T}$ in ${\mathbb{H}}^3$ such that

1.  The 