We propose and study a model for $N$ hard-core bosons which allows for the interpolation between one- and high-dimensional behavior by variation of just a single external control parameter $s/t$. It consists of a ring-lattice of $d$ sites with a hopping rate $t$ and an extra site at its center... Increasing the hopping rate $s$ between the central site and the ring sites induces a transition from the regime of a quasi-condensed number $N_0$ of bosons proportional to $\sqrt{N}$ to complete condensation with $N_0 \simeq N$. In the limit $s/t \to 0, d \to \infty$ with $\tilde{s}=(s/t)\sqrt{d}$ fixed the low-lying excitations follow from an effective ring-Hamiltonian. An excitation gap makes the condensate robust against thermal fluctuations at low temperatures. These findings are supported and extended to the full parameter regime by large scale density matrix renormalization group computations. We show that ultracold bosonic atoms in a Mexican-hat-like potential represent an experimental realization allowing to observe the transition from quasi to complete condensation by creating a well at the hat's center. (read more)