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tokens: the difference to Cuzzi et al. ( 2010 )’s assumption that the grains would be sized to optimally couple to the smallest eddies and questioned whether the pebble concentrations in Cuzzi et al. ( 2010 )’s semi-analytic model exceeded what is physically plausible. If the assumptions in Cuzzi et al. ( 2010 ) are unrealistic and if Hopkins ( 2016 )’s modelling and assumptions capture all the important physics, then larger numbers of, and better known orbits for the ultra-wide binaries could constrain whether the turbulent concentration mechanism produces excessively large planetesimals that would have disrupted the TNOs. Pebble Accretion is a promising mechanism for growing planetesimals and protoplanets (Ormel Klahr 2010 ; Lambrechts Johansen 2012 ). It substantially enhances the cross-section for accreting small particles that are partially coupled to the gas and have their relative velocities damped by gas drag (see Johansen Lambrechts 2017 , for a review). Johansen et al. ( 2015 ) considered the evolution of a population of planetesimals growing by pebble accretion. They began with a size distribution of large bodies derived from simulations of the Streaming Instability (Youdin Goodman 2005 ; Johansen et al. 2007 ), which produces q ∼ 2.8 with a maximum mass of (Simon et al. 2016 , 2017 ). Johansen et al. ( 2015 ) considered the subsequent evolution of the planetesimals in this environment. They performed simulations of a narrow ring at 25 au and found that a single body underwent significant growth, reaching roughly an Earth mass, amounting to roughly one-third of the mass in that ring. If this result for a single 3 M ⊕ ring can be extended to a 30 M ⊕ disc spanning 20–30 au, the disc would produce ∼10 Earth mass bodies, inconsistent with the limits derived here. Whether this result is generally applicable to Pebble Accretion depends on the sensitivity of final mass-number distribution to factors such as the initial mass-number distribution, which is yet to be broadly explored. Similar to Pebble Accretion, the collisional pebble agglomeration model of Shannon, Wu Lithwick ( 2016 ) also produces a top heavy q ∼ 2 size number distribution, but with the largest bodies in the 10 s to 100 s of kilometers in size, dependent on the composition of the pebbles. Here, we use the code and general setup from that work, but consider a belt from 20 to 30 au that begins with 30 M ⊕ . With little mass in bodies larger than ∼100 km, it is compatible with the limits we have found. In addition to testing planetesimal formation models, our limits offer constraints on the dynamical history of the solar system. Several other works have invoked large bodies within the pre-Scattered disc to explain features of the Solar system. As described in Section 1 , Nesvorný Vokrouhlický ( 2016 ) invoked 1000–4000 bodies of mass or 1000 objects of mass in the pre-Scattered disc to produce the inferred capture rate of resonant objects. These choices would be incompatible with the