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A fundamental problem in crystallisation, and in molecular tile-based self-assembly in particular, is how to simultaneously control its two main constituent processes: seeded growth and spontaneous nucleation. Often, we desire out-of-equilibrium growth without spontaneous nucleation, which can be achieved through careful calibration of temperature, concentration and experimental time-scale a laborious and overly-sensitive approach. Another technique is to find alternative nucleation-resistant tile designs [Minev et al, 2001]. Rogers, Evans and Woods [In prep] propose blockers: short DNA strands designed to dynamically block DNA tile sides, altering self-assembly dynamics. Experiments showed independent and tunable control on nucleation and growth rates. Here, we provide a theoretical explanation for these surprising results. We formally define the kBlock model where blockers bind to tiles at thermodynamic equilibrium in solution and stochastic kinetics allow self-assembly of a tiled structure. In an intentionally simplified mathematical setting we show that blockers permit reasonable seeded growth rates, akin to a non-blocked tile system at lower tile concentration, crucially giving nucleation rates that are exponentially suppressed. We then implement the kBlock model in a stochastic simulator, with results showing remarkable alignment with oversimplified theory. We provide evidence of blocker-induced tile buffering, where a large reservoir of blocked tiles slowly feeds a small unblocked tile subpopulation which acts like a regular, non-blocked, low tile concentration system, yet is capable of long-term buffered assembly. Finally, and perhaps most satisfyingly, theory and simulations align remarkably well with DNA self-assembly experiments over a wide range of concentrations and temperatures, matching the size of growth temperature windows to within 12%. Blockers are a straightforward solution to the challenging problem of simultaneously and independently controlling growth and nucleation, using a motif compatible with many DNA tile systems.