<p>Magic, or nonstabilizerness, quantifies the distance of a quantum state from stabilizer states and serves as a resource for quantum computational advantage. Here, we investigate magic transitions in measurement-only quantum circuits comprising competing Clifford and non-Clifford measurements. Remarkably, this circuit can be mapped onto a classical model, enabling efficient large-scale numerical simulations and exact characterization of magic using measures that are additive for tensor products of single-qubit states. We identify a magic transition between two phases exhibiting extensive magic, separated by a critical point where mutual magic displays scaling analogous to entanglement entropy. Additionally, these distinct phases can be distinguished by topological magic. In contrast, with a vanishing rate of non-Clifford measurements, the system exhibits saturation of magic. Our results clarify the nature of magic and its linear combinations in quantum circuits utilizing genuine magic measures, thereby advancing our understanding of quantum complexity in monitored quantum systems.</p>